Quantum Fisher information matrix and multiparameter estimation
arXiv:1907.08037 · doi:10.1088/1751-8121/ab5d4d
Abstract
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér-Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cramér-Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.
arXiv comment~70 pages, close to published version, open access
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- Ultimate Quantum Precision Limit at Colliders: Conditions and Case Studies
- Optimal quantum precision in noise estimation: Is entanglement necessary?
- Quantum metrology through spectral measurements in quantum optics
- Coherence-Mediated Quantum Thermometry in a Hybrid Circuit-QED Architecture
- Precision Bounds for Characterising Quantum Measurements
- On the categorical foundations of quantum information theory: Categories and the Cramer-Rao inequality
- G-dual teleparallel connections in Information Geometry
- Optimal Hamiltonian recognition of unknown quantum dynamics
- Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information
- Nonequilibrium thermometry via an ensemble of initially correlated qubits
- Generalized uncertainty relation between thermodynamic variables in quantum thermodynamics
- Gill and Massar type bound for estimation of channel
- Information geometry of bosonic Gaussian thermal states
- Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
- Momentum-resolved two photon interference of weak coherent states
- Reference-frame-independent quantum metrology
- Role of overparametrization in quantum approximate optimization
- Enhancement of quantum sensing in a dissipatively coupled two-mode system
- Spontaneous Scattering of Raman Photons from Cavity-QED Systems in the Ultrastrong Coupling Regime
- Metrological approach to the emergence of classical objectivity
- Gaussian quantum metrology in a dissipative environment
- Optimal Displacement Sensing with Spin-Dependent Squeezed States
- Enhanced Quantum Metrology via Saddle-Point Scrambling in Phase Space
- Information geometry of nonmonotonic quantum natural gradient
- Natural gradient and parameter estimation for quantum Boltzmann machines
- Bounds on quantum Fisher information and uncertainty relations for thermodynamically conjugate variables
- Probing parameters estimation with Gaussian non-commutative measurements
- Trade-off relation between integrated metrological gain and local dissipation in magnetic-field sensing by quantum spin ensemble
- Experimental Joint Estimation of Phase and Phase Diffusion via Deterministic Bell Measurements
- Direct temperature readout in nonequilibrium quantum thermometry
- Universal Operational Privacy in Distributed Quantum Sensing
- Graphene Josephson Junctions for Engineering Motional Quanta
- Optimal noisy quantum phase estimation with finite-dimensional states
- Sensitivity Bounds of Multiparameter Metrology at Thermal Equilibrium
- Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation
- Quantum Speed Limits and the Ultimate Scaling of the Quantum Sensors
- Resilience-Runtime Tradeoff Relations for Quantum Algorithms
- From Independent to Joint: Enhancing Quantum Phase and Correlation Factor Estimation by Squeezed Reservoir Engineering
- Characterization and generation of a SQL-beating catlike state through repetitive measurements
- Optimal finite-dimensional probe states for quantum phase estimation
- Quantum-enhanced passive remote sensing
- Measurement compatibility in multiparameter quantum interferometry
- Quantum reading of quantum information
- Toward Witnessing Molecular Exciton Entanglement from Spectroscopy
- Approaching the Multiparameter Quantum Cramér-Rao Bound via Classical Correlation and Entangling Measurements
- Revisit on quantum parameter estimation approach for Mach-Zehnder interferometry
- Superresolution of unequal-brightness thermal sources for stellar interferometry
- Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds
- Estimating Bell Diagonal states with separable measurements
- Uncertainty-disturbance relations and applications
- Photon self-interaction through gravitons and axions
- Dynamics of Quantum Coherence and Non-Classical Correlations in Open Quantum System Coupled to a Squeezed Thermal Bath
- Quantum limits to resolution and discrimination of spontaneous emission lifetimes
- Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution